N-dimensional extension of unfold-PCA for granular systems monitoring

This work is focused on the data based modelling and monitoring of a family of modular systems that have multiple replicated structures with the same nominal variables and show temporal behaviour with certain periodicity. These characteristics are present in many systems in numerous fields such as the construction or energy sector or in industry. The challenge for these systems is to be able to exploit the redundancy in both time and the physical structure. In this paper the authors present a method for representing such granular systems using N-dimensional data arrays which are then transformed into the suitable 2-dimensional matrices required to perform statistical processing. Here, the focus is on pre-processing data using a non-unique folding-unfolding algorithm in a way that allows for different statistical models to be built in accordance with the monitoring requirements selected. Principal Component Analysis (PCA) is assumed as the underlying principle to carry out the monitoring. Thus, the method extends the Unfold Principal Component Analysis (Unfold-PCA or Multiway PCA), applied to 3D arrays, to deal with N-dimensional matrices. However, this method is general enough to be applied in other multivariate monitoring strategies. Two of examples in the area of energy efficiency illustrate the application of the method for modelling. Both examples illustrate how when a unique data-set folded and unfolded in different ways, it offers different modelling capabilities. Moreover, one of the examples is extended to exploit real data. In this case, real data collected over a two-year period from a multi-housing social-building located in down town Barcelona (Catalonia) has been used This work has been carried out by the research group eXIT (http://exit.udg.edu), funded through the following projects: MESC project(Ref. DPI2013-47450-C21-R) and its continuation CROWDSAVING (Ref.TIN2016-79726-C2-2-R), both funded by the Spanish Ministerio de Industria y Competitividad within the Research, Development and Innovation Program oriented towards the Societal Challenges, and also the project Hit2Gap of the Horizon 2020 research and innovation program under grant agreement N680708. The author Llorenç Burgas would also like to thank Girona University for their support through the competitive grant for doctoral formation IFUdG2016